On convergence rates in approximation theory for operator semigroups |
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Authors: | Alexander Gomilko Yuri Tomilov |
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Institution: | 1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland;2. Institute of Mathematics, Polish Academy of Sciences, ?niadeckich 8, 00-956 Warszawa, Poland |
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Abstract: | We create a new, functional calculus, approach to approximation formulas for C0-semigroups on Banach spaces restricted to the domains of fractional powers of their generators. This approach allows us to equip the approximation formulas with rates which appear to be optimal in a natural sense. In the case of analytic semigroups, we improve our general results obtaining better convergence rates which are optimal in that case too. The setting of analytic semigroups includes also the case of convergence on the whole space. As an illustration of our approach, we deduce optimal convergence rates in classical approximation formulas for C0-semigroups restricted to the domains of fractional powers of their generators. |
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Keywords: | Bernstein functions Approximation of C0-semigroups" target="_blank">gif" overflow="scroll">C0-semigroups Functional calculus Convergence rates Banach spaces Interpolation |
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